Note that in order for the connection between the single tensor and the three boundary wormhole to be sharp, we require that the interior region is large enough that there are no other competing entanglement wedge cross sections except the horizons of \(A\)  and \(B\)  since there is no analog of such surfaces in the single tensor. It seems plausible that this can be arranged for by adding sufficient matter in the interior to support a long wormhole like in Ref. [1]}.
